So you think that will be more beneficial than actually running the 2 miles with a long sprint at the end of the run? I will be on a treadmill

Absolutely. I know it's more difficult to do on a treadmill, so what you could do instead is go by mileage. E.g. .20 miles regular pace (say 7.5mph), followed by .10 miles at almost a sprint (9mph). This way you don't have to change settings quite so much. When I'm looking to decrease my run times I use this method and it works. Usually it's better to work on distance first, then speed. Additionally, it's usually good to take a week off after the first 2-3 weeks to allow some time for your body to heal, but it looks like you're on a tight timetable.